Finite Group DatabasebetaFinite Group Databasebeta| order | 22688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C709 ⋊ #131 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11344 |
Polycyclic presentation:
2^5,709|a^2=d,d^2=e,f^a=f^96,c^b=ce,f^d=f^708905 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22688, 233);